One of the most interesting things about printmaking is the way you can get your lines to interact with each other. This is particularly relevant in both wood block and linoleum printing. These two forms of printing are both very affected by the way you choose to carve in to them. Carving all of the lines parallel, or carving the lines irregular, will both show up in a final print.
Controlling how your line work shows through in your work leads to authentic and complex looking images. When layering prints, these lines will interact to create a sense of depth and intensity. If sloppy, the lines can become confusing and distracting. Exercising control requires a good amount of patience. Carving a block is a process and it can easily to become frustrating, which causes carelessness.
Though line work is usually lacking from a screen print you can get a similar effect if you hand draw your screens. The line work will come through in hatching, but it will not really show in quite the same way as the previously mentioned forms of printing.
To utilize line work in your practice it is important to choose the right form of printing. Pick something you are comfortable with and concentrate on how you are carving.
With a little practice and patience, you will have be able to use the line work to your advantage.
Some artists to look at: German Expressionists
Above are examples of my layered woodblock prints.